Profiles and polarizations of the Balmer-αline from high-temperature hydrogen atoms in strong magnetic fields

Energies and eigenstates are obtained for the $n=2\mathrm{}$ and $n=3\mathrm{}$ levels of hydrogen atoms moving in strong magnetic fields. The Hamiltonian of the system includes the interaction with the Lorentz field, $\overrightarrow{E}=\overrightarrow{\mathrm{v}}\times \overrightarrow{B}$, as well as the magnetic interaction, $-\overrightarrow{\mu }·\overrightarrow{B}$. These results are utilized together with the Doppler shifts in order to obtain profiles and polarizations of the Balmer-$\alpha$ line in tokamak-like environments under the assumption that the velocity distributions are Maxwellian.